package weka.filters.timeseries;

/* Performs a FFT of the data set. NOTE:
 * 1. If algorithm type is set to DFT, then this will only perform a FFT if the series is length power of 2.
 * otherwise it will perform the order m^2 DFT.
 * 2. If algorithm type is set to FFT, then, if the length is not a powerr of 2, it either truncates or pads 
 * (determined by the variable pad) with the mean the each series (i.e. each Instance) 
 * so that the new length is power of 2 by flag pad (default true)
 * 2. By default, stoAlgorithmTyperes the complex terms in order, so att 1 is real coeff of Fourier term 1, attribute 2 the imag etc
 * 3. Only stores the first half of the Fourier terms (which are duplicates of the second half)
 * 
 * Note that the series does store the first fourier term (series mean) and the 
 * imaginary part will always be zero
 */
import weka.core.*;
import weka.filters.SimpleBatchFilter;

public class FFT extends SimpleBatchFilter {
	/**
	 * 
	 */
	public enum AlgorithmType {
		DFT, FFT
	} // If set to DFT, this will only perform a FFT if the series is length
		// power of 2, otherwise resorts to DFT

	AlgorithmType algo = AlgorithmType.DFT; // If set to FFT, this will pad (or
											// truncate) series to the nearest
											// power of 2
	private static final long serialVersionUID = 1L;
	private boolean pad = true;
	private static final double TWOPI = (Math.PI * 2);

	public void padSeries(boolean b) {
		pad = b;
	}

	public void useDFT() {
		algo = AlgorithmType.DFT;
	}

	public void useFFT() {
		algo = AlgorithmType.FFT;
	}

	@Override
	protected Instances determineOutputFormat(Instances inputFormat) throws Exception {
		// Check all attributes are real valued, otherwise throw exception
		for (int i = 0; i < inputFormat.numAttributes(); i++)
			if (inputFormat.classIndex() != i)
				if (!inputFormat.attribute(i).isNumeric())
					throw new Exception("Non numeric attribute not allowed in FFT");
		/**
		 * This method determines whether padding is required. The If the DFT is
		 * being calculated, the length will be 2*m, where m= (numAttributes -1)
		 * If the FFT is being used if pad ==true find x=first ^2 greater than m
		 * length=x else find x=first ^2 greater than m , y last ^2 less than m
		 * length= min(x-m,m-y)
		 **/
		int length = findLength(inputFormat);

		// Set up instances size and format.

		FastVector atts = new FastVector();
		String name;
		for (int i = 0; i < length; i++) {
			if (i % 2 == 0)
				name = "FFT_" + (i / 2) + "_Real";
			else
				name = "FFT_" + (i / 2) + "_Imag";
			atts.addElement(new Attribute(name));
		}
		if (inputFormat.classIndex() >= 0) { // Classification set, set class
			// Get the class values as a fast vector
			Attribute target = inputFormat.attribute(inputFormat.classIndex());

			FastVector vals = new FastVector(target.numValues());
			for (int i = 0; i < target.numValues(); i++)
				vals.addElement(target.value(i));
			atts.addElement(new Attribute(inputFormat.attribute(inputFormat.classIndex()).name(), vals));
		}
		Instances result = new Instances("FFT_" + inputFormat.relationName(), atts, inputFormat.numInstances());
		if (inputFormat.classIndex() >= 0)
			result.setClassIndex(result.numAttributes() - 1);
		return result;
	}

	protected int findLength(Instances inputFormat) {
		if (algo == AlgorithmType.FFT)
			return findPowerOfTwoLength(inputFormat);
		else if (algo == AlgorithmType.DFT) {
			if (inputFormat.classIndex() >= 0) { // Classification set, dont
													// transform the target
													// class!
				return (inputFormat.numAttributes() - 1);
			} else
				return inputFormat.numAttributes();
		}
		throw new RuntimeException("Aglorithm Type+ " + algo + " has not been implemented for FFT Class");
	}

	// Length of the series NOT COUNTING THE CLASS ATTRIBUTE
	protected int findPowerOfTwoLength(Instances inputFormat) {
		int oldLength = 0;
		int length = 0;
		if (inputFormat.classIndex() >= 0) // Classification set, dont transform
											// the target class!
			oldLength = inputFormat.numAttributes() - 1;
		else
			oldLength = inputFormat.numAttributes();
		// Check if a power of 2, if not either pad or truncate
		if (!MathsPower2.isPow2(oldLength)) {
			length = (int) MathsPower2.roundPow2((float) oldLength);
			if (pad) {
				if (length < oldLength)
					length *= 2;
			} else {

				if (length > oldLength)
					length /= 2;
			}
		} else
			length = oldLength;
		return length;

	}

	@Override
	public String globalInfo() {

		return null;
	}

	/**
	 * 
	 * @param instances
	 * @return Fourier transforms, each consecutive two terms are the
	 *         real/imaginary
	 * @throws Exception
	 *             This process only stores half the Fourier terms, since the
	 *             second half are just a duplicate of the first half with a
	 *             different sign for the imaginary term If the DFT algorithm is
	 *             used, it returns exactly m terms (where m is the original
	 *             series length If FFT is used it returns x/2, where x is
	 *             either the smallest power of 2 greater than m (padding), or
	 *             the largest power of 2 less than m (truncating). If the
	 *             variable pad is true, it ALWAYS pads, if pad==false it will
	 *             go to the closest power of 2 above or below.
	 */

	@Override
	public Instances process(Instances instances) throws Exception {

		Instances output = determineOutputFormat(instances);

		int originalLength = instances.numAttributes();
		if (instances.classIndex() >= 0) {
			originalLength--;
		}
		// Get the length of the full complex series, which might be padded or
		// truncated.
		int fullLength = findLength(instances);
		// For each data, first extract the relevant data
		// Note the transform will be at least twice as long as the original
		// Length is the number of COMPLEX terms, which is HALF the length of
		// the original series.

		for (int i = 0; i < instances.numInstances(); i++) {

			// 1. Get original series stored in a complex array. This may be
			// padded or truncated
			// depending on the original length. If DFT is being used, it is
			// neither.
			Complex[] c = new Complex[fullLength];
			int count = 0;
			double seriesTotal = 0;
			for (int j = 0; j < originalLength && count < c.length; j++) { // May
																			// cut
																			// off
																			// the
																			// trailing
																			// values
				if (instances.classIndex() != j) {
					c[count] = new Complex(instances.instance(i).value(j), 0.0);
					seriesTotal += instances.instance(i).value(j);
					count++;
				}
			}
			// Add any Padding required
			double mean = seriesTotal / count;
			while (count < c.length)
				c[count++] = new Complex(mean, 0);
			// 2. Find FFT/DFT of series.
			if (algo == AlgorithmType.FFT)
				fft(c, c.length);
			else
				c = dft(c);
			// Extract out the terms and set the attributes.

			Instance inst = new DenseInstance(c.length + 1);
			for (int j = 0; j < c.length / 2; j++) {
				inst.setValue(2 * j, c[j].real);
				inst.setValue(2 * j + 1, c[j].imag);
			}
			// Set class value.
			// Set class value.
			if (instances.classIndex() >= 0)
				inst.setValue(output.classIndex(), instances.instance(i).classValue());

			output.add(inst);
		}
		return output;
	}

	/**
	 * Perform a discrete fourier transform, O(n^2)
	 * 
	 */
	public Complex[] dft(double[] series) {
		int n = series.length;
		Complex[] dft = new Complex[n];
		for (int k = 0; k < n; k++) { // For each output element
			float sumreal = 0;
			float sumimag = 0;
			for (int t = 0; t < series.length; t++) { // For each input element
				sumreal += series[t] * Math.cos(2 * Math.PI * t * k / n);
				sumimag += -series[t] * Math.sin(2 * Math.PI * t * k / n);
			}
			dft[k] = new Complex(sumreal, sumimag);
		}
		return dft;

	}

	public Complex[] dft(Complex[] complex) {
		int n = complex.length;
		Complex[] dft = new Complex[n];
		for (int k = 0; k < n; k++) { // For each output element
			float sumreal = 0;
			float sumimag = 0;
			for (int t = 0; t < complex.length; t++) { // For each input element
				sumreal += complex[t].real * Math.cos(2 * Math.PI * t * k / n) + complex[t].imag * Math.sin(2 * Math.PI * t * k / n);
				sumimag += -complex[t].real * Math.sin(2 * Math.PI * t * k / n) + complex[t].imag * Math.cos(2 * Math.PI * t * k / n);
			}
			dft[k] = new Complex(sumreal, sumimag);
		}
		return dft;

	}

	/**
	 * Perform an in-place mixed-radix inverse Fast Fourier Transform on the
	 * first <code>n</code> elements of the given set of <code>Complex</code>
	 * numbers. If <code>n</code> is not a power of two then the inverse FFT is
	 * performed on the first N numbers where N is largest power of two less
	 * than <code>n</code>
	 */
	public void fft(Complex[] complex, int n) {
		fft(1, complex, n);
	}

	/**
	 * Sort a set of <code>Complex</code> numbers into a bit-reversed order -
	 * only sort the first <code>n</code> elements. This method performs the
	 * sort in-place
	 */
	public static void bitReverse(Complex[] complex, int n) {
		int halfN = n / 2;
		int i, j, m;
		Complex temp;
		for (i = j = 0; i < n; ++i) {
			if (j >= i) {
				temp = complex[j];
				complex[j] = complex[i];
				complex[i] = temp;
			}
			m = halfN;
			while (m >= 1 && j >= m) {
				j -= m;
				m /= 2;
			}
			j += m;
		}
		temp = null;
	}

	/**
	 * Perform an in-place mixed-radix inverse Fast Fourier Transform on the
	 * first <code>n</code> elements of the given set of <code>Complex</code>
	 * numbers. If <code>n</code> is not a power of two then the inverse FFT is
	 * performed on the first N numbers where N is largest power of two less
	 * than <code>n</code>
	 */
	public void inverseFFT(Complex[] complex, int n) {
		fft(-1, complex, n);
	}

	// Perform an in-place mixed-radix FFT (if sign is 1) or inverse
	// FFT (if sign is -1) on the first n elements of the given set of
	// Complex numbers. Round n to the nearest power of two.
	//
	// This method performs the FFT in-place on the given set.

	private void fft(int sign, Complex[] complex, int n) {
		// n is number of data elements upon which FFT will be
		// performed. Round number of data elements to nearest power
		// of 2
		n = (int) MathsPower2.roundPow2(n);
		// Sort the first n elements into bit-reversed order
		bitReverse(complex, n);
		if (n == 2) {
			// Perform a radix-2 FFT
			radix2FFT(sign, complex, n, 0);
		} else if (((float) Math.log(n) % (float) Math.log(4)) == 0) {
			// Perform a radix-4 FFT
			radix4FFT(sign, complex, n, 0);
		} else {
			// n is a multiple or two or four [8, 32, 128, ...]
			// Perform a mixed-radix FFT
			int halfN = n / 2;
			// Do a radix-4 transform on elements 0..halfN - 1 which
			// contains even-indexed elements from the original
			// unsorted set of numbers by definition of the bit
			// reversal operation
			radix4FFT(sign, complex, halfN, 0);
			// Do a radix-4 transform on elements halfN - 1 .. n - 1
			// which contains odd-indexed elements from the original
			// unsorted set of numbers by definition of the bit
			// reversal operation
			radix4FFT(sign, complex, halfN, halfN);
			// Pair off even and odd elements and do final radix-2
			// transforms, multiplying by twiddle factors as required
			// Loop variables used to point to pairs of even and odd
			// elements
			int g, h;
			// Array of two complex numbers for performing radix-2
			// FFTs on pairs of elements
			Complex[] radix2x2 = new Complex[2];
			// Twiddle factor
			Complex twiddle = new Complex();
			// Values defining twiddle factor
			double delta = -sign * TWOPI / n;
			double w = 0;
			for (g = 0, h = halfN; g < halfN; g++, h++) {
				// Twiddle factors...
				twiddle.setRealImag((float) Math.cos(w), (float) Math.sin(w));
				complex[h].multiply(twiddle);
				radix2x2[0] = complex[g];
				radix2x2[1] = complex[h];
				// Perform the radix-2 FFT
				radix2FFT(sign, radix2x2, 2, 0);
				complex[g] = radix2x2[0];
				complex[h] = radix2x2[1];
				w += delta;
			}
			radix2x2 = null;
			twiddle = null;
		}
		if (sign == -1) {
			// Divide all values by n
			for (int g = 0; g < n; g++) {
				complex[g].divide(n);
			}
		}
	}

	// Perform an in-place radix-4 FFT (if sign is 1) or inverse
	// FFT (if sign is -1). FFT is performed in the n elements
	// starting at index lower
	//
	// Assumes that n is a power of 2 and that lower + n is less than
	// or equal to the number of complex numbers given
	//
	// This method performs the FFT in-place on the given set.

	private static void radix4FFT(int sign, Complex[] complex, int n, int lower) {
		// Index of last element in array which will take part in the
		// FFT
		int upper = n + lower;
		// Variables used to hold the indicies of the elements forming
		// the four inputs to a butterfly
		int i, j, k, l;
		// Variables holding the results of the four main operations
		// performed when processing a butterfly
		Complex ijAdd = new Complex();
		Complex klAdd = new Complex();
		Complex ijSub = new Complex();
		Complex klSub = new Complex();
		// Twiddle factor
		Complex twiddle = new Complex();
		// Values defining twiddle factor
		double delta, w, w2, w3;
		double deltaLower = -sign * TWOPI;
		// intraGap is number of array elements between the
		// two inputs to a butterfly (equivalent to the number of
		// butterflies in a cluster)
		int intraGap;
		// interGap is the number of array elements between the first
		// input of the ith butterfly in two adjacent clusters
		int interGap;
		for (intraGap = 1, interGap = 4 * intraGap; intraGap < n; intraGap = interGap, interGap = 4 * intraGap) {
			delta = deltaLower / (float) interGap;
			// For each butterfly in a cluster
			w = w2 = w3 = 0;
			for (int but = 0; but < intraGap; ++but) {
				// Process the intraGap-th butterfly in each cluster
				// i is the top input to a butterfly and j the second,
				// k third and l fourth
				for (i = (but + lower), j = i + intraGap, k = j + intraGap, l = k + intraGap; i < upper; i += interGap, j += interGap, k += interGap, l += interGap) {
					// Calculate and apply twiddle factors
					// cos(0) = 1 and sin(0) = 0
					twiddle.setRealImag(1, 0);
					complex[i].multiply(twiddle);
					twiddle.setRealImag((float) Math.cos(w2), (float) Math.sin(w2));
					complex[j].multiply(twiddle);
					twiddle.setRealImag((float) Math.cos(w), (float) Math.sin(w));
					complex[k].multiply(twiddle);
					twiddle.setRealImag((float) Math.cos(w3), (float) Math.sin(w3));
					complex[l].multiply(twiddle);
					// Compute the butterfly
					Complex.add(complex[i], complex[j], ijAdd);
					Complex.subtract(complex[i], complex[j], ijSub);
					Complex.add(complex[k], complex[l], klAdd);
					Complex.subtract(complex[k], complex[l], klSub);
					// Assign values
					Complex.add(ijAdd, klAdd, complex[i]);
					klSub.multiply(sign);
					complex[j].setRealImag(ijSub.getReal() + klSub.getImag(), ijSub.getImag() - klSub.getReal());
					Complex.subtract(ijAdd, klAdd, complex[k]);
					complex[l].setRealImag(ijSub.getReal() - klSub.getImag(), ijSub.getImag() + klSub.getReal());
				}
				w += delta;
				w2 = w + w;
				w3 = w2 + w;
			}
			intraGap = interGap;
		}
		ijAdd = klAdd = ijSub = klSub = twiddle = null;
	}

	// Perform an in-place radix-2 FFT (if sign is 1) or inverse
	// FFT (if sign is -1). FFT is performed in the n elements
	// starting at index lower
	//
	// Assumes that n is a power of 2 and that lower + n is less than
	// or equal to the number of complex numbers given...
	//
	// This method performs the FFT in-place on the given set.

	private static void radix2FFT(int sign, Complex[] complex, int n, int lower) {
		// Index of last element in array which will take part in the
		// FFT
		int upper = n + lower;
		// Variables used to hold the indicies of the elements forming
		// the two inputs to a butterfly
		int i, j;
		// intraGap is number of array elements between the
		// two inputs to a butterfly (equivalent to the number of
		// butterflies in a cluster)
		int intraGap;
		// interGap is the number of array elements between the first
		// input of the ith butterfly in two adjacent clusters
		int interGap;
		// The twiddle factor
		Complex twiddle = new Complex();
		// Values defining twiddle factor
		float deltaLower = -(float) (sign * Math.PI);
		float w, delta;
		// Variable used to hold result of multiplying butterfly input
		// by a twiddle factor
		Complex twiddledInput = new Complex();
		for (intraGap = 1, interGap = intraGap + intraGap; intraGap < n; intraGap = interGap, interGap = intraGap + intraGap) {
			delta = deltaLower / (float) intraGap;
			// For each butterfly in a cluster
			w = 0;
			for (int butterfly = 0; butterfly < intraGap; ++butterfly) {
				// Calculate the twiddle factor
				twiddle.setRealImag((float) Math.cos(w), (float) Math.sin(w));
				// i is the top input to a butterfly and j the
				// bottom
				for (i = (butterfly + lower), j = i + intraGap; i < upper; i += interGap, j += interGap) {
					// Calculate the butterfly-th butterfly in
					// each cluster
					// Apply the twiddle factor
					Complex.multiply(complex[j], twiddle, twiddledInput);
					// Subtraction part of butterfly
					Complex.subtract(complex[i], twiddledInput, complex[j]);
					// Addition part of butterfly
					complex[i].add(twiddledInput);
				}
				w += delta;
			}
			intraGap = interGap;
		}
		twiddle = twiddledInput = null;
	}

	public String getRevision() {
		return null;
	}

	public static class MathsPower2 {

		/** Return 2 to the power of <code>power</code> */

		public static int pow2(int power) {
			return (1 << power);
		}

		/** Is <code>value</code> a power of 2? */

		public static boolean isPow2(int value) {
			return (value == (int) roundPow2(value));
		}

		/** Round <code>value</code> to nearest power of 2 */

		public static float roundPow2(float value) {
			float power = (float) (Math.log(value) / Math.log(2));
			int intPower = Math.round(power);
			return (float) (pow2(intPower));
		}

		/**
		 * Return the log to base 2 of <code>value</code> rounded to the nearest
		 * integer
		 */

		public static int integerLog2(float value) {
			int intValue;
			if (value < 2) {
				intValue = 0;
			} else if (value < 4) {
				intValue = 1;
			} else if (value < 8) {
				intValue = 2;
			} else if (value < 16) {
				intValue = 3;
			} else if (value < 32) {
				intValue = 4;
			} else if (value < 64) {
				intValue = 5;
			} else if (value < 128) {
				intValue = 6;
			} else if (value < 256) {
				intValue = 7;
			} else if (value < 512) {
				intValue = 8;
			} else if (value < 1024) {
				intValue = 9;
			} else if (value < 2048) {
				intValue = 10;
			} else if (value < 4098) {
				intValue = 11;
			} else if (value < 8192) {
				intValue = 12;
			} else {
				intValue = Math.round(roundPow2(value));
			}
			return intValue;
		}
	}

	/**
	 * Remove all attributes unless the target class I'm not sure if the
	 * indexing changes
	 * 
	 * @param n
	 */
	public void truncate(Instances d, int n) {
		int att = n;
		if (att < d.numAttributes() - 1) {// Remove the first two terms first
			d.deleteAttributeAt(0);
			d.deleteAttributeAt(0);
		}
		while (att < d.numAttributes()) {
			if (att == d.classIndex())
				att++;
			else
				d.deleteAttributeAt(att);
		}
	}

	public static void computeDft(double[] inreal, double[] inimag, double[] outreal, double[] outimag) {
		int n = inreal.length;
		for (int k = 0; k < n; k++) { // For each output element
			double sumreal = 0;
			double sumimag = 0;
			for (int t = 0; t < n; t++) { // For each input element
				sumreal += inreal[t] * Math.cos(2 * Math.PI * t * k / n) + inimag[t] * Math.sin(2 * Math.PI * t * k / n);
				sumimag += -inreal[t] * Math.sin(2 * Math.PI * t * k / n) + inimag[t] * Math.cos(2 * Math.PI * t * k / n);
			}
			outreal[k] = sumreal;
			outimag[k] = sumimag;
		}
	}

	/** Author Mike Jackson - University of Edinburgh - 1999-2001 */

	/**
	 * The <code>Complex</code> class generates objects that represent complex
	 * numbers in terms of real and imaginary components and supports addition,
	 * subtraction, multiplication, scalar multiplication and division or these
	 * numbers. The calculation of complex conjugates, magnitude, phase and
	 * power (in decibels) of the <code>Complex</code> numbers are also
	 * supported.
	 */

	public static class Complex implements Cloneable {

		/** Constant required to calculate power values in dBs: log 10 */

		protected static final float LOG10 = (float) Math.log(10);

		/**
		 * Constant required to calculate power values in dBs: 20 / log 10
		 */

		protected static final float DBLOG = 20 / LOG10;

		/** Real component */

		protected float real;

		/** Imaginary component */

		protected float imag;

		/** Create a new <code>Complex</code> number 0 + j0 */

		public Complex() {
			real = imag = 0f;
		}

		/**
		 * Create a new <code>Complex</code> number <code>real</code> + j(
		 * <code>imag</code>)
		 */

		public Complex(float real, float imag) {
			this.real = real;
			this.imag = imag;
		}

		public String toString() {
			return real + "+" + imag + "*i";
		}

		public Complex(double real, double imag) {
			this.real = (float) real;
			this.imag = (float) imag;
		}

		/**
		 * Set the <code>Complex</code> number to be <code>real</code> + j(
		 * <code>imag</code>)
		 */

		public void setRealImag(float real, float imag) {
			this.real = real;
			this.imag = imag;
		}

		/** Get real component */

		public float getReal() {
			return real;
		}

		/** Set real component */

		public void setReal(float real) {
			this.real = real;
		}

		/** Get imaginary component */

		public float getImag() {
			return imag;
		}

		/** Set imaginary component */

		public void setImag(float imag) {
			this.imag = imag;
		}

		/**
		 * Add the given <code>Complex</code> number to this
		 * <code>Complex</code> number
		 */

		public void add(Complex complex) {
			real += complex.real;
			imag += complex.imag;
		}

		/**
		 * Subtract the given <code>Complex</code> number from this
		 * <code>Complex</code> number
		 */

		public void subtract(Complex complex) {
			real -= complex.real;
			imag -= complex.imag;
		}

		/**
		 * Multiply this <code>Complex</code> number by the given factor
		 */

		public void multiply(float factor) {
			real *= factor;
			imag *= factor;
		}

		/** Divide this <code>Complex</code> number by the given factor */

		public void divide(float factor) {
			real /= factor;
			imag /= factor;
		}

		/**
		 * Multiply this <code>Complex</code> number by the given
		 * <code>Complex</code> number
		 */

		public void multiply(Complex complex) {
			float nuReal = real * complex.real - imag * complex.imag;
			float nuImag = real * complex.imag + imag * complex.real;
			real = nuReal;
			imag = nuImag;
		}

		/**
		 * Set this <code>Complex</code> number to be its complex conjugate
		 */

		public void conjugate() {
			imag = (-imag);
		}

		/**
		 * Return result of adding the complex conjugate of this
		 * <code>Complex</code> number to this <code>Complex</code> number
		 */

		public float addConjugate() {
			return real + real;
		}

		/**
		 * Return result of subtracting the complex conjugate of this
		 * <code>Complex</code> number from this <code>Complex</code> number
		 */

		public float subtractConjugate() {
			return imag + imag;
		}

		/** Return the magnitude of the <code>Complex</code> number */

		public float getMagnitude() {
			return magnitude(real, imag);
		}

		/** Return the phase of the <code>Complex</code> number */

		public float getPhase() {
			return phase(real, imag);
		}

		/** Return the power of this <code>Complex</code> number in dBs */

		public float getPower() {
			return power(real, imag);
		}

		/** Add two <code>Complex</code> numbers: c = a + b */

		public static void add(Complex a, Complex b, Complex c) {
			c.real = a.real + b.real;
			c.imag = a.imag + b.imag;
		}

		/** Subtract two <code>Complex</code> numbers: c = a - b */

		public static void subtract(Complex a, Complex b, Complex c) {
			c.real = a.real - b.real;
			c.imag = a.imag - b.imag;
		}

		/**
		 * Multiply a <code>Complex</code> number by a factor: b = a * factor
		 */

		public static void multiply(Complex a, float factor, Complex b) {
			b.real = a.real * factor;
			b.imag = a.imag * factor;
		}

		/**
		 * Divide a <code>Complex</code> number by a factor: b = a / factor
		 */

		public static void divide(Complex a, float factor, Complex b) {
			b.real = a.real / factor;
			b.imag = a.imag / factor;
		}

		/** Multiply two <code>Complex</code> numbers: c = a * b */

		public static void multiply(Complex a, Complex b, Complex c) {
			c.real = a.real * b.real - a.imag * b.imag;
			c.imag = a.real * b.imag + a.imag * b.real;
		}

		/** Place the <code>Complex</code> conjugate of a into b */

		public static void conjugate(Complex a, Complex b) {
			b.real = a.real;
			b.imag = -a.imag;
		}

		/**
		 * Return the magnitude of a <code>Complex</code> number
		 * <code>real</code> + (<code>imag</code>)j
		 */

		public static float magnitude(float real, float imag) {
			return (float) Math.sqrt(real * real + imag * imag);
		}

		/**
		 * Return the phase of a <code>Complex</code> number <code>real</code> +
		 * (<code>imag</code>)j
		 */

		public static float phase(float real, float imag) {
			return (float) Math.atan2(imag, real);
		}

		/**
		 * Return the power of a <code>Complex</code> number <code>real</code> +
		 * (<code>imag</code>)j
		 */

		public static float power(float real, float imag) {
			return DBLOG * (float) Math.log(magnitude(real, imag));
		}

		/**
		 * Place the real components of the first <code>n</code> elements of the
		 * array <code>complex</code> of <code>Complex</code> numbers into the
		 * given <code>reals</code> array
		 */

		public static void reals(int n, Complex[] complex, float[] reals) {
			for (int i = 0; i < n; ++i) {
				reals[i] = complex[i].real;
			}
		}

		/**
		 * Place the imaginary components of the first <code>n</code> elements
		 * of the array <code>complex</code> of <code>Complex</code> numbers
		 * into the given <code>imags</code> array
		 */

		public static void imaginaries(int n, Complex[] complex, float[] imags) {
			for (int i = 0; i < n; ++i) {
				imags[i] = complex[i].imag;
			}
		}

		/**
		 * Place the magnitudes of the first <code>n</code> elements of the
		 * array <code>complex</code> of <code>Complex</code> numbers into the
		 * given <code>mags</code> array
		 */

		public static void magnitudes(int n, Complex[] complex, float[] mags) {
			for (int i = 0; i < n; ++i) {
				mags[i] = complex[i].getMagnitude();
			}
		}

		/**
		 * Place the powers (in dBs) of the first <code>n</code> elements of the
		 * array <code>complex</code> of <code>Complex</code> numbers into the
		 * given <code>powers</code> array
		 */

		public static void powers(int n, Complex[] complex, float[] powers) {
			for (int i = 0; i < n; ++i) {
				powers[i] = complex[i].getPower();
			}
		}

		/**
		 * Place the phases (in radians) of the first <code>n</code> elements of
		 * the array <code>complex</code> of <code>Complex</code> numbers into
		 * the given <code>phases</code> array
		 */

		public static void phase(int n, Complex[] complex, float[] phases) {
			for (int i = 0; i < n; ++i) {
				phases[i] = complex[i].getPhase();
			}
		}

		/** Return a clone of the <code>Complex</code> object */

		public Object clone() {
			return new Complex(real, imag);
		}
	}

	// Primitives version, assumes zero mean global, passes max run length
	public int[] processSingleSeries(double[] d, int mrl) {

		return null;
	}

	public static void basicTest() {
		// Test FFT
		// Series 30,-1,2,3,3,2,-1,-4
		/*
		 * FFT Desired 34 19.9289321881345-5.82842712474618i 32-2i
		 * 34.0710678118655+0.171572875253798i 34
		 * 34.0710678118655-0.171572875253815i 32+2i
		 * 19.9289321881345+5.8284271247462i FFT Achieved 34 0 19.928932
		 * -5.8284273 32 -2 34.071068 0.17157269 34 0 34.071068 -0.17157269 32 2
		 * 19.928932 5.8284273
		 */
		// Test FFT with truncation
		System.out.println("Basic test of FFT");

		System.out.println("Series: 30,-1,2,3,3,2,-1,-4");
		System.out.println("	/*FFT Desired" + "  	34\n" + "19.9289321881345-5.82842712474618i\n" + "32-2i\n" + "34.0710678118655+0.171572875253798i\n" + "34\n" + "34.0710678118655-0.171572875253815i\n" + "32+2i\n" + "19.9289321881345+5.8284271247462i\n" + "FFT Achieved\n" + "34	0\n" + "19.928932	-5.8284273\n" + "32	-2\n" + "34.071068	0.17157269\n" + "34	0\n" + "34.071068	-0.17157269\n" + "32	2\n" + "19.928932	5.8284273");
		double[] d = { 30, -1, 2, 3, 3, 2, -1, -4 };
		int n = 8;
		Complex[] x = new Complex[n];
		for (int i = 0; i < n; i++)
			x[i] = new Complex(d[i], 0.0);
		for (int i = 0; i < n; i++)
			System.out.println(x[i].getReal() + "," + x[i].getImag());
		System.out.println("Transformed");

		FFT fft = new FFT();
		fft.fft(x, x.length);
		for (int i = 0; i < n; i++)
			System.out.println(x[i].getReal() + "," + x[i].getImag());
		fft.fft(x, x.length);
	}

	public static void paddingTest() {
		/*
		 * Test to check it works correctly with padded series //Series
		 * 30,-1,2,3,3,2,-1,-4,3 //Padded series 30,-1,2,3,3,2,-1,-4,3,0,0,0,0,
		 */
	}

	public static void main(String[] args) {
		// basicTest();
		FFT fft = new FFT();
		int size = 8;
		double[] testSeries = new double[size];
		for (int i = 0; i < size; i++) {
			testSeries[i] = Math.random();
		}
		Complex[] dft = fft.dft(testSeries);
		Complex[] dft2 = new Complex[size];
		for (int i = 0; i < size; i++)
			dft2[i] = new Complex(testSeries[i], 0);
		Complex[] dft3 = fft.dft(dft2);
		for (int i = 0; i < size; i++)
			System.out.println(dft[i] + "   :::   " + dft3[i]);
		System.exit(0);

		matlabComparison();
	}

	/*
	 * Comparison to running the Matlab script FFT_Testing
	 */
	public static void matlabComparison() {

		// MATLAB Output generated by
		// Power of 2: use FFT
		// Create set of instances with 16 attributes, with values
		// Case 1: All Zeros
		// Case 2: 1,2,...16
		// Case 3: -8,-7, -6,...,0,1,...7
		// Case 4: 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1
		// Instances
		// test1=ClassifierTools.loadData("C:\\Users\\ajb\\Dropbox\\TSC Problems\\TestData\\FFT_test1");
		/*
		 * Instances test2=ClassifierTools.loadData(
		 * "C:\\Users\\ajb\\Dropbox\\TSC Problems\\TestData\\FFT_test2");
		 * Instances t2; try{ // t2=fft.process(test1); //
		 * System.out.println(" FFT ="+t2); fft.padSeries(true);
		 * t2=fft.process(test2); System.out.println(" FFT with padding="+t2);
		 * fft=new FFT(); fft.padSeries(false); t2=fft.process(test2);
		 * System.out.println(" FFT with truncation="+t2); fft=new FFT();
		 * fft.useDFT(); t2=fft.process(test2); System.out.println(" DFT ="+t2);
		 * 
		 * 
		 * }catch(Exception e){ System.out.println(" Errrrrrr = "+e);
		 * e.printStackTrace(); System.exit(0); }
		 */
		// Not a power of 2: use padding

		// Not a power of 2: use truncate

		// Not a power of 2: use DFT

	}

}
